

A258205


Number of strictly nonoverlapping holeless polyhexes of perimeter 2n with bilateral symmetry, counted up to rotation.


5



0, 0, 1, 0, 1, 1, 3, 1, 8, 5, 20, 11, 61
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OFFSET

1,7


COMMENTS

This sequence counts by perimeter length those holeless polyhexes that stay same when they are flipped over and rotated appropriately.
For n >= 1, a(n) gives the total number of terms k in A258005 with binary width = 2n + 1, or equally, with A000523(k) = 2n.


LINKS

Table of n, a(n) for n=1..13.


FORMULA

Other identities and observations. For all n >= 1:
a(n) = 2*A258206(n)  A258204(n).
a(n) <= A258018(n).


PROG

(Scheme)
(define (A258205 n) (let loop ((k (+ 1 (expt 2 (+ n n)))) (c 0)) (cond ((pow2? k) c) (else (loop (+ 1 k) (+ c (if (isA258005? k) 1 0)))))))
(define (pow2? n) (let loop ((n n) (i 0)) (cond ((zero? n) #f) ((odd? n) (and (= 1 n) i)) (else (loop (/ n 2) (1+ i)))))) ;; Gives nonfalse only when n is a power of two.
;; Code for isA258005? given in A258005.


CROSSREFS

Cf. A057779, A258005, A258018, A258204, A258206.
Sequence in context: A172157 A209136 A206800 * A258018 A188939 A062196
Adjacent sequences: A258202 A258203 A258204 * A258206 A258207 A258208


KEYWORD

nonn,more


AUTHOR

Antti Karttunen, May 31 2015


STATUS

approved



